When we superpose two simple harmonic movements with perpendicular directions, we obtain a planar movement that is described by the equations x = A1 * cos(w1*t) y = A2 * cos(w2*t + d) where the A's denote the amplitudes of the respective movements (horizontal the first one, vertical the second), the w's denote the respective frequencies and d denotes the phase delay between both movements.

If we supply these two signals to the horizontal and vertical inputs of an oscilloscope, its beam will describe a movement that is the result of the superposition of both individual movements and that can adopt several nice figures, depending on the value of the ratio w1/w2 and on d.

These curves are called Lissajous' figures and are specially nice for certain values of the parameters.

Author : Francisco Esquembre

Date : February 2002

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